Techniques of both these articles rely heavily on a correspondence between the quaternionic manifold and its twistor space, which is a complex manifold and thus one can apply the Hirzebruch-Riemann-Roch theorem. Our approach is more elementary and computational in nature, the main tool is a version of the Atiyah-Singer index theorem for elliptic complexes associated to a \(G\) -structure. The theorem provides us with a topological formula involving several characteristic classes but to simplify this we need some "common language." Luckily, this was described in [1]}, where a quaternionic structure is viewed as an action of a bundle of quaternion algebras. Using this and the method of Borel and Hirzebruch (see [2]}) for computation of Chern classes, we have developed an algorithm how to obtain a formula for the analytical index for each given complex and in each given dimension.
